FIGURE 6.54 ■ A magnetic accelerometer. 6.18 Magnetic accelerometer. A magnetic accelerometer is made as shown in Figure 6.54. A coil with N = 500 turns carries a current I = 10 mA, wound around the moving mass but allowing the mass full freedom to move. A spring that can act either in tension or in compression keeps the mass in place with a gap of 2 mm between its surface and the surface of the Hall sensor on the stationary pole. The latter is made of iron, 15 mm in diameter, has high relative perme- ability so that the reluctance of iron can be neglected, and the mass of the moving core is 10 g. a. If the sensor must be capable of sensing accelerations up to 100 g in each direction, what is the spring constant? bobog Spring L= 10 mA Coil 0,5 mm Iron core N = 500 turns 2 mm Iron frame Hall element a b. If the Hall element used is connected to a current I and is d mm thick, cal- culate the sensitivity of the sensor as a function of acceleration and the cur- rent in the Hall element. Assume the Hall coefficient is known. c. A silicon Hall element, 0.5 mm thick with a Hall coefficient of -0.01 m³/A - S is used, driven with a 5 mA current. Calculate the span of the output of the sensor and its sensitivity over the span.